How many factors of 48886966800 are odd numbers?

M4maths Previous Puzzles

26 Jan 2018 ODD Number

How many factors of 48886966800 are odd numbers?

OPtion

1) 120
2) 80
3) 160
4) 180
5) 210
6) 240
7) 125
8) 144
9) 150
10) None of these

Solution

48886966800 = 53^1 * 83^1 * 7^3 * 5^2 * 2^4 * 3^4

Any factor of this number should be of the form 53^a * 83^b * 7^c * 5^d * 2^e * 3^f.

For the factor to be an odd number e should be 0.

a can take values 0, 1
b can take values 0, 1
c can take values 0, 1, 2, 3
d can take values 0, 1, 2
e can take values 0
and f can take values 0, 1, 2, 3, 4

Total number of odd factors = 2*2*4*3*1*5 = 240

Option 6)

Correct Option: 6 Best Solution (0)